Appreciation of Ultra-visible Quantities. 417 



Jo a certain distance along a free path, in the intervals 

 between their encounters with one another ; and information 

 as to the average length of these little journeys can be 

 deduced from experiments on the viscosity of gases. If the 

 gas is a tolerably "perfect" one; at the ordinary tempera- 

 ture ; and exposed to the pressure of one atmosphere, the 

 average length of the " f ree path " of the molecules is small. 

 In fact the observed amount of the viscosity assigns to it in 

 air a length equal to the ordinate of our gauge at a distance 

 of something like three quarters of a metre (30 inches) from 

 its apex ; and although the mean length of the free path 

 differs from one gas to another, it is in all a magnitude of 

 this order*. Note that this is a good deal smaller than what 

 we have found to be the u minimum visibile." 



Within the receiver of an air-pump the free path becomes 

 longer, until at the excessive attenuations that Mr. Crookes 

 obtains by working his compound Sprengel-pump for a long 

 time, its average length may even reach to several centi- 

 metres, which would be the ordinate of our gauge at 

 a distance from its apex of some hundreds of miles. Pon- 

 derable matter is then in what Mr. Crookes calls the radiant 

 state. 



2. The average spacing of the molecules in a gas (i. e. their 

 average distance asunder at any one instant of time) may be 

 obtained in various ways f ; e. g. it may be deduced from the 



* See Philosophical Magazine for August 1868, p. 138. 



t Calling the average length of the free path X, the average interval 

 between the molecules cr, and the average "diameter of a molecule" 8; 

 Ave can obtain X from experiments on viscosity, we get S/cr from observing 

 the condensation which the gas undergoes when liquehed, and one other 

 equation between X, <r, and 8 would enable us to obtain all three. 



Now it is evident that X (the average length of the journeys of the 

 molecules) will, cceteris paribus, increase if <r (the space between the 

 molecules) is increased, which may be effected by expanding the gas, and 

 will decrease if h (the distance within which the molecules sensibly act 

 on one another) is increased, which may be effected by exchanging one 

 gas for another. It is, in fact, a function of these two quantities and of 

 others, viz. of the velocities of the molecules (the mean of the squares of 

 which is known from the pressure and density of the gas), of the events 

 that occur in the struggle of two molecules with one another during their 

 brief encounters, and of the time occupied by these struggles. 



The events that occur during the encounters and the time they last are 

 not sufficiently known for the actual equation to be set down : but hypo- 

 theses can be framed in regard to them — as, for instance, that the mole- 

 cules when they encounter simply rebound like hard elastic globes —which 

 enable us to ascertain what function a/X would be of ft/o- if the hypothesis 

 were true, and thus enable us to judge what kind of magnitudes d and 

 o- are. 



The quantities X and S vary within wide limits from gas to gas ; but it 

 is one of the elementary propositions in the kinetic theory of gases that cr 



